THEORIES  OF  METALLIC  CONDUCTION  OE 
ELECTRICITY  WITH  EXPERIMENTS 
ON  THE  CONDUCTIVITY  OF  A 
RO  FATING  COIL 

; BY 

CLARENCE  CARL  SCHMIDT 
B.  A.  Cornell  College  i q 1 7 


THESIS 

Submitted  in  Partial  Fulfillment  of  the  Requirements  for  the 

Degree  of 

MASTER  OF  ARTS 

IN  PHYSICS 
IN 

THE  GRADUATE  SCHOOL 
OF  THE 

UNIVERSITY  OE  ILLINOIS 


1921 


Digitized  by  the  Internet  Archive 
in  2016 


https://archive.org/details/theoriesofmetallOOschm 


[ 


TABLE  OF  CONTENTS 


I  INTRODUCTION*  • • 1 

II  EARLY  THEORIES  OF  METALLIC  CONDUCTION  1 

III  ELECTRONIC  THEORIES  4 

The  Free  Gas  Theory 
Thomson's  Doublet  Theory 


Pressure  Exp er im ent s and  "Gap”  Theory  of  Bridgeman 
IV  EXPERIMENTS  WITH  MECHANICAL  FORCES  ON  ELECTRONS.  • . .13 


V EXPERIMENTS  BY  THE  WRITER 15 

VI  SUMMARY  AND  CONCLUSIONS 36 

VII  BIBLIOGRAPHY 28 


I INTRODUCTION 

how  does  an  electric  current  pass  through  a metallic  wire? 

This  most  common  of  electrical  occurrences  presents  an  unsolved 
fundamental  problem  in  electrical  science.  In  tne  passage  of  the 
current  through  electrolytic  and  gaseous  conductors,  the  theories 
seem  fairly  complete  and  satisfactory.  Experiments  nave  shown  that 
the  electric  current  carried  through  electrolytes  ana  gases  is  accom- 
panied by  the  transfer  of  material  particles  or  ions  and  it  has  been 
proved  by  varied  and  ingenous  experiments  that  the  electric  transfer 
is  a convection  process. 

For  metallic  conduction,  there  is  as  yet  no  explanation  which 
may  be  regarded  as  at  all  adequate  and  complete.  It  is  the  purpose 
of  this  paper  to  present  and  discuss  the  various  theories  of  metallic 
conduction  ana  to  describe  a new  experiment  which  has  given  results 
that  seem  to  be  of  importance  in  tne  problem. 

II  EARLY  THEORIES 

Probably  the  first  theory  of  metallic  conduction  was  formulated 

by  Wilhelm  weoer  (d4)  who  assumed  that  two  equal  streams  of  positive 

. 

and  negative  electricity  flowed  in  opposite  directions.  The  elec- 
tricity would  continually  bp  accelerated  by  the  electromotive  force, 
if  there  were  no  resistance.  This  resistance  according  to  Y/eber  is 
caused  by  the  attraction  of  the  opposing  electrical  masses.  If  now 
a positive  and  a negative  particle  approach  each  other  there  will  be 
an  attraction,  between  them,  similar  to  that  between  two  bodies  at- 
tracted oy  gravity.  The  particles  will  under  such  action  describe 
spiral  paths  about  a common  center.  The  applied  electromotive  force 
causes  the  paths  of  the  rotating  system  to  be  drawn  out  longitudinal- 
ly sc  that  the  particles  come  into  the  sphere  of  influence  of 


3 


neighboring  systems  to  which  tney  escape.  New  systems  are  thus  formec 
and  by  a continuous  process  the  electric  current  is  carried  through 
the  length  of  the  conductor. 

Herwig  (bb)  conceives  the  stream  of  electricity  as  a movement 
of  the  electrical  particles  from  one  molecule  to  another  and.  the  re- 
sistance as  the  force  of  opposition  encountered  in  moving  from  one 
atom  to  another.  This  involves  a Change  in  the  amplitude  of  vibra- 
tion of  the  particles  as  well  as  a movement  in  the  direction  of  the 
electromotive  force.  Both  of  these  phenomena  require  a certain 
amount  of  work;since  the  movement  of  the  particles  carrying  the  cur- 
rent requires  that  the  amplitude  change  also,  and  since  heating  of 
the  conductor  increases  the  energy  of  vibration,  then  heating  should 
increase  the  resistance  of  a conductor. 

Another  theory  of  metallic  conduction  of  electricity  was  that 
the  charge  was  carried  by  molecules,  out  in  the  case  of  dense  solids, 
such  as  the  metals,  such  a process  is  hardly  conceivable,  since  noth- 
ing as  large  as  a molecule  could  pass  through  the  metal  with  such 
ease  as  must  be  the  case,  because  the  forces  required  to  send  a cur- 
rent through  a wire  are  small. 

From  this  it  is  seen  that  some  other  carrier  must  be  found  to 
account  for  the  passage  of  a current.  Giese  (10)  was  one  of  the 
first  to  form  a different  theory.  He  argued  against  the  molecular 
transfer  theory,  since  if  molecules  were  acting  as  the  carriers  there 
must  be  a large  amount  of  matter  carried  with  the  current.  it  had 
been  determined  previously  that  the  passage  of  electricity  through 
flames  was  by  means  of  charged  atoms,  hence  it  was  argued  that  atoms 
might  perform  tne  same  office  of  carriers  in  the  case  of  metals.  In 

order  to  produce  the  same  effect  by  means  of  a charged  molecule 


| PJ.H  3ai^  . ■ 


. 


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' 

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3 


several  thousand  times  (at  least  1700  times  in  the  case  of  hydrogen' 
as  much  more  matter  would  have  to  be  transferred  as  in  the  case 
where  tne  ions  are  given  this  property. 

Furthermore,  he  snows  that  the  molecule  cannot  be  electrified. 
Water  is  an  example  which  readily  shows  this.  Distilled  water  has 
very  high  insulating  properties,  but  wnen  used  as  a solvent  its  ions 
according  to  Giese  become  highly  conducting. 

According  to  his  tnecry,  a given  substance  or  metal  may  nave 
atoms  wnich  are  exactly  alike  except  for  tneir  cnarges,  for  in- 
stance, Cu+  and  Cu_.  The  property  of  being  a conductor  or  a non- 
conductor depends  upon  tne  relative  number  of  each  kind.  The  mole- 
cules may  excnange  ions  and  thus  the  excess  charges  will  find  their 
way  to  the  surface. 

When  two  metals  are  placed  in  contact,  the  excess  ions  on 
each  tend  to  neutralize  each  other.  An  e.m.f.  would  then  be  pro- 
duced, the  magnitude  of  whicn  would  depend  upon  tne  kind  of  metals 
that  were  placed  in  contact.  These  excess  ions  were  termed  "free 
ions"  on  account  of  being  free  to  move  about  and  thus  carry  the 
current.  The  difference  between  metallic  and  electrolytic  conduc- 
tion is  that  in  the  latter,  tne  ions  bodily  carry  the  charge  from 
place  to  place,  while  in  the  former,  the  charge  is  passed  along  by 
the  int ercnanging  of  ions  between  tne  molecules.  The  metals  being 
of  denser  material,  the  molecules  are  bound  to  remain  in  one  place 
and  are  not  free  to  move  as  in  tne  case  of  tne  electrolyte;  hence, 
there  is  merely  a shift  of  ions  from  one  to  the  other. 

The  difference,  according  to  this  theory,  between  conductors 
and  insulators  is,  that  the  latter  have  no  free  icns,  or  tnat  each 
ion  is  bound  to  a particular  molecule  and  cannot  Change  to  another. 


. 

- 
. 


. . . 


. 


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■ ■ 

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4 


A cnange  in  the  resistance  indicates  a molecular  cnange  such  tnat 
the  metal  eitner  becomes  more  conductive,  or  offers  more  resistance 
according  as  tne  number  of  free  ions  becomes  greater  or  less. 

Such  a theory  tho  explaining  some  things  very  well  was  far 
from  satisfactory.  Numerous  experiments  were  made  to  determine 
whether  there  was  any  transfer  of  matter  with  the  passage  of  a cur- 
rent. Two  metals  were  placed  in  contact  and  a current  passed 
through  them  for  a long  time,  in  one  case  for  tne  space  of  a whole 
year;  but  no  trace  of  either  metal  could  be  found  in  the  other. 

These  earlier  theories  have,  of  course,  been  antiquated  by 
the  discovery  of  the  electron.  They  are  , however,  important  in 
being  the  direct  forerunners  of  our  present  electron  theories  of 
conduction.  Indeed,  when  these  earlier  theories  are  translated  in- 
to tne  language  of  tne  electronic  theory,  they  are  very  suggestive 
and  in  some  cases  show  anticipation  of  our  more  recent  ideas. 


III.  ELECTRONIC  THEORIES  OF  CONDUCTION 


The  study  of  the  conduction  of  electricity  tnrougn  gases  whic.  i 
was  extended  about  this  time  threw  new  light  upon  the  subject,  es- 
pecially when  the  electron  was  discovered  by  J.J.  Thomson  and  oth- 
ers about  189?.  It  was  shown  that  this  was  the  basic  particle  of 
electric lty  whicn  might  move  and  carry  the  current  through  the 
metal.  Its  small  size,  nign  velocity,  and  the  fact  that  electrons 

are  the  same  in  every  metal  made  it  tne  logical  carrier  of  elec- 
tricity. 


Riecke  (24)  carries  out  an  iaea  expressed. 


tnough  not  develop  i 


by  Weber  (34)  who  stated  years  before  that  the  molecules  of  a metal 


were  surrounded  by  moving  molecules  or  particles  of  electricity. 


. 


- 

- 

■ 

. 


. 


. 


. . 

. 


' 

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5 

These  particles  Riecke  identifies  as  tne  electrons  or  corpuscles 
discovered  tnrough  the  work  of  J.J.  Thomson  and  others. 

Drude  (8)  added  considerable  to  tne  ideas  of  Riecke  and 
showed  a marked  similarity  between  these  ideas  and  the  ideas  ex- 
pressed by  Giese.  The  properties  of  carrying  tne  current  ascribed 
by  tne  latter  to  the  ion,  Drude  points  out  belong  to  the  electron, 
tne  cnarge  unattached  to  any  matter.  These  electrons  seem  to  ocey 
the  kinetic  theory  of  gases  and  hence  Drude' s theory  is  known  as  the 
"free  gas"  theory. 

Since  metals  are  the  best  conductors  of  both  electricity  and 
heat,  the  electron  must  play  a part  in  the  conduction  of  both  heat 
and  electricity.  The  fact  that  electrons  or  one  metal  do  not  diriei 
from  those  of  another  strengthens  this  viewpoint.  When  the  coef- 
ficients of  thermal  and  electrical  conductivities  are  compared 
there  is  found  to  be  a constant  ratio  between  them.  This  had  been 
noted  many  years  before  and  is  known  as  the  Wiedemann  - Franz' (38) 
ratio;  questions  have  been  raised  about  the  significance  of  this 
ratio,  but  it  has  been  shown  to  be  a fact  both  theoretically  and 
experimentally.  There  is  also  a marked  parallelism  between  the 
change  of  thermal  and  electrical  conductivity  with  temperature. 

A gas  is  considered  as  having  molecules  moving  in  ail  direc- 
tions ana  if  the  number  is  taken  as  N,  then  in  each  of  the  six  di- 
rections parallel  to  the  three  axes  there  are  M/6  moving  with  a 
velocity  v.  Each  molecule  has  a momentum  +mv  on  striking  a surface 
and  -mv  on  rebounding  from  it.  The  pressure  on  the  surface  is 
Nv/6  x 2mv  or  P = 1/3  Nmv2 . Mm  is  the  mass  per  unit  volume  of  gas 
or  the  density. 

But,  pressure  x volume  = RT 


. 


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6 

or  1/5  Nmvi 2  = RT. 

This  snows  that  the  kinetic  energy  is  proportional  to  the  absolute 
temperature  or  1 Jd  mv2  = °c  T where  c<=  5/2  R/N.  Thus  when  electrons 
in  a ooncluctor  are  in  temperature  equilibrium  the  velocity  may  be 
found  from  the  kinetic  theory. 

£e 

The  acceleration  of  an  electron  after  collision  is  f = — wfter e 
E is  the  electrical  intensity.  The  average  distance  traveled  by  an 
electron,  or  the  mean  free  path  is  A,  hence  the  distance  traveled  due 
to  the  acceleration,  f,  is 

1 Ee  Af_ 

2 m va 

where  ^ is  the  time  taken  to  traverse  the  mean  free  path  in  the  di- 
rection of  tne  field.  The  average  velocity  m this  direction  is 

1 Ee  A2  v _1  EeA 

2 m v2  A 2 mv 

but  mv2  = <=*  T or  m = ~~ 

2 v2 

Therefore  the  average  velocity  in  the  direction  of  the  field 
E e A v 


is 


4°c  T 


Tne  corresponding  current,  is  i\ie  times  the  velocity  where  J5J  is 
the  number  of  electrons  per  unit  volume,  or 

current  = = i 

4°<  T 

i N e2  A v 

and  conductivity,  <r  = g-  = —^-5^  * 

It  follows  that  Onm's  law  is  ooeyea,  for  the  conductivity  is  inde- 
pendent of  the  current  and  further  the  conductivity  is  inversely  pro- 
portional to  the. absolute  temperature. 

In  a very  similar  way  the  thermal  conductivity  k,  is  found  to 
be  hv<*  A 


7 


The  ratio  of  k/j-  is  tnen  given  as 

Nvoc  A 


5 

he2  Av 
4<*T 


= Cx)2  |t 


Experimental  results  show  tnat  this  ratio  witn  very  few  exceptions  is 
constant,  ana  its  value  is  given  as  6.5  x IQ10. 

Wnen  an  electric  force  is  appliea  tnere  is  a arnt  oi  electrons 
in  tne  airection  of  the  force.  If  the  parts  of  the  metal  are  at  dif- 
ferent temperatures  the  heat  will  flow  from  the  hotter  parts  to  the 
cold.  If  the  greater  part  of  the  heat  conductivity  is  due  to  elec- 
trons the  thermal  conductivity  should  hear  a constant  ratio  to  elec- 
trical conductivity. 

If  an  electric  current  passes  through  an  unequally  heated  metal 
electrons  will  drift  from  places  of  high  potential  to  low  potential 
and  carry  heat  with  them;  thus  the  passage  of  a current  through  a 
conductor  will  alter  the  flow  of  heat.  This  is  known  as  the  Thomson 
effect  discovered  by  Sir  Wm.  Thomson,  Lord  Kelvin. 

J.J.  Thomson  (30)  in  noting  the  effect  of  temperature  on  the 
resistance  of  metals  finds  that  the  free  gas  theory  is  inadequate. 

If  the  electrical  conductivity  is  due  to  free  electrons,  changes  in 
conductivity  are  due  to  two  factors,  n,  the  number  of  free  electrons 
and,k,  their  mobility.  The  product  of  n and  k,  if  the  conductivity 

is  inversely  proportional  to  the  absolute  temperature,  must  be  greater 

~ w 

'*"*  TTTrr 

at  low  temperatures  than  at  high.  Since  n is  proportional  to  e 
where  T is  the  absolute  t emperature  temperature  and  H the  gas  con- 
stant, and,  since  this  factor  decreases  at  low  temperatures,  then 
the  increase  in  nk  must  be  due  to  k,  or  tne  mobility  of  the  system. 
But  this  he  finds  must  also  decrease  witn  lowering  temperature. 


, 

. 

. 

. 


. 


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■ 

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• 

• 

' " ' 

^ A . . O - * - 


Y-fifriilS  '-iX  j.1 


-x  ;-s  ? • I J... 


, 


8 


Experiments  by  Kammerlingh  Onnes  (29)  with  metals  at  low  tem- 
peratures seern  to  contradict  the  free  electron  theory.  He  found  that 
the  resistance  of  pure  metala,  sucn  as  lead  or  mercury,  at  the  tem- 
perature of  liquid  helium  becomes  so  small  that  it  cannot  be  measured, 
or  less  than  one  thousandth-millionth  of  its  value  at  0°C.  In  the 
case  of  a lead  ring  a current  started  by  moving  a magnet  up  to  the 
coil  will  continue  for  some  time  without  any  very  noticeable  decrease 
if  the  low  temperature  is  maintained.  In  fact,  it  was  estimated  that 
the  current  would  continue  for  four  days  before  it  would  fall  to  one 
half  its  value. 

In  view  of  the  difficulties  thus  involved  in  tne  free  gas  theo- 
ry, Thomson  (29,31)  introduced  another,  analogous  to  the  molecular 
theory  of  magnetism.  He  shows  in  this  that  the  presence  of  a nega- 
tive charge  means  that  there  is  also  an  equal  positive  charge.  Each 
molecule  of  the  metal  has  an  electric  dipole  consisting  of  equal  and 
opposite  electric  charges  a short  distance  apart.  When  an  electric 
force  is  applied  these  dipoles  align  themselves  in  chains  extending 
in  the  direction  of  the  electric  force  from  one  end  of  the  conductor 
to  the  other.  These  doublets  will  produce  strong  electric  forces 
which  will  tend  to  pull  the  electron  from  one  atom  to  another.  The 
difference  between  a conductor  and  an  insulator  lies  in  the  power  to 
resist  the  electric  force.  In  the  case  of  metals  this  is  much  less 
than  in  the  case  of  insulators. 

The  superconductivity  noticed  by  Onnes  (30)  in  which  the  re- 
sistance drops  down  very  suddenly  to  practically  zero  may  be  ex- 
plained in  that  the  electric  force  polarizes  the  dipoles  in  the  metal 
which  then  remain  in  that  state  wnen  cooled,  even  though  the  electric 
force  is  removed;  hence,  the  current  will  still  persist. 


9 

In  measuring  the  effect  of  increased  pressure  in  twenty  two 
metals  Bridgeman  (2)  found  that  with  the  exception  of  two,  namely, 
antimony  and  bismuth,  the  increase  in  pressure  tends  to  decrease  the 
resistance.  He  found,  however,  that,  though  under  pressure  of,  say, 
12,000  Kg  and  at  a temperature  of  0°C  the  volume  is  smaller  than  at 
0°  absolute.  Nevertheless,  the  decrease  in  resistance  at  that  pres- 
sure is  a very  small  percent  of  the  change  in  resistance  brought 
about  when  tne  metal  is  cooled  to  0°  absolute,  a point  toward  which 
the  resistance  tends  to  approach  zero.  In  the  case  of  the  two  abnor- 
mal metals  mentioned  the  change  in  volume  due  to  pressure  of  12,000 
is  almost  three  times  tne  change  in  volume  due  to  cooling  to  0° 
absolut  e. 

In  regard  to  the  theory  of  Brude,  Riecke  and  Lcrentz,  which  ex- 
presses the  conductivity  in  the  form 

conductivity  = constant  g— 
or 

conductivity  = constant  — 

N 

wnere  N is  the  number  of  electrons  per  cubic  centimeter,  1,  the  mean 

free  path,  u,  the  velocity,  ana  T,  the  absolute  temperature, 

Bridgeman  (6)  says  it  fails  to  account  satisfactorily  for  specific 

heat,  tne  variation  of  resistance  with  temperature,  and  the  negative 

pressure  coefficient  at  constant  temperature.  The  values  of  N,  1, 

and  u,  cannot  under  any  circumstances  be  conceived  as  changing  enough 

to  account  for  the  change  in  resistance.  According  to  J.J.  Thomson's 

doublet  theory  the  conductivity  is  given  by 

n _ 1 N epdM 
C ~ 3 KT 

where  N is  the  number  of  doublets  per  cubic  centimeter,  p,  the  numbei 
of  electrons  emitted  by  an  atom  per  second,  M,  the  moment  of  the 


. 


. 

. 


10 


doublet,  K,  tne  gas  constant,  ana  d,  the  distance  between  tne  centers 

of  adjacent  atoms.  Part  of  the  increase  might  be  accounted  for  a 

change  in  N.  But,  according  to  Richardson,  N for  tungsten  at  2000° 

16 

is  1.7  x 10  which  tends  to  be  the  minimum  value,  ana  tnis  number  is 
much  too  large  to  justify  tne  equation;  hence,  he  concludes  that  this 
theory  is  inadequate. 

The  equation  developed  by  Grdneisen  (11)  is  the  only  one  wnich 
in  any  way  provides  for  pressure  effects.  It  is  given  as 

u^TF^T  = u(“F)  s * s + Ws  ~ c^H^P  \}  +C*T  TJ- 

in  which  u is  tne  velocity  of  the  electrons  and  — (i^)a  is  a relation 

U h?  ° 

between  pressure  ana  velocity  which  is  unknown.  The  electrical  re- 
sistance of  a pure  metal  is  proportional  to  a universal  function  of 
T/  vm  where  vm  is  determined  by  tne  atomic  temperature.  Grdneisen 
found  tnat  the  experimental  results  of  Lissell,  Williams,  LaFay, 
Beckman,  Chwolson,  Tomlinson  and  others  agree  with  this  equation. 

According  to  this  tneory  of  Grdneisen  the  movement  of  the  elec- 
trons increases  witn  the  compression  of  the  atoms  wnile  the  amplitude 

of  vibration  decreases.  This  is  also  the  viewpoint  of  Bridgeman  who 

* 

states  also  that  the  cnange  in  resistance  may  be  due  to  a change  in 
the  amplitude  of  vibration  of  the  atoms. 

Be  proposes  a different  tneory  for  tne  resistance  offered  to 
the  passage  of  electrons.  In  the  free  gas  theory  this  is  explained 
as  due  to  the  friction  of  the  electrons,  or  the  collision  of  the 
electrons  with  the  molecules,  wisn  thought  of  it  as  caused  by  the 
collision  of  the  electrons  with  the  positive  neucleous. 

Bridgeman  (6),  on  tne  otner  hand,  departs  radically  from  this 
and  says  that  no  resistance  is  offered  to  the  electron  as  if  passes 
through  tne  molecule,  bux  tnat  the  resistance  is  explained  as  due  to 


11 


a force  which  is  required  to  move  the  electron  from  one  atom  to  an- 
other. He  calls  this  tne  "gap"  theory,  he  snows  that  the  electron 
encounters  difficulty  in  getting  away  from  the  atom,  as  may  oe  seen 
from  the  fact  that  there  is  a definite  ionizing  potential  in  the  case 
of  a gas.  This  force  which  tends  to  act  against  the  passage  of  an 
electron  from  atom  to  atom  is  less,  the  smaller  the  mean  free  path,  and 
since  this  depends  upon  tne  amplitude  of  vibration,  tnen  tne  amount 
of  resistance  can  be  traced  directly  to  this  amplitude  of  vibration. 

The  classical  expression  for  the  resistance  R = —f — will  hold 

e3nl 

where,  e is  the  cnarge,  ana  v the  velocity  of  the  electron.  Ohm’s 
law  can  also  be  explained  by  this  theory. 

In  support  of  this  theory  Bridgeman  shows  that  where  the  metal 
changes  tne  state  of  aggregation  as  in  melting,  the  state  wnicn  has 
the  smaller  volume  has  the  least  resistance.  This  is  snown  to  be 
tirue  not  only  in  the  case  of  metals  which  act  normally  upon  melting, 
but  also  for  those  in  which  abnormalities  occur  as  in  Bi,  Sb,  and  Ga, 

in  which  tne  liquid  has  tne  lesser  volume  ana  tne  smaller  resistance. 

He  holds  that  this  is  more  easily  explained  from  tne  "gap”  point  of 
view  tnan  from  Wien’s  in  which  collision  with  the  atomic  center  forms 
the  basis  of  explanation. 

He  points  out  tnat  in  the  classical  theory  1,  ana  v were  de- 
termined, but  n was  made  to  fit  as  the  case  demanded  without  snowing 

sufficient  reason  for  the  change  in  n.  In  the  gap  theory  variations 
in  v and  1 are  accounted  for;  hence,  there  is  no  necessity  for  chang- 
ing the  value  of  n,  wnich  is  therefore  assumed  to  remain  constant. 

Bridgeman  applies  the  "gap"  theory  to  a number  of  different  ef- 
fects to  snow  that  it  is  not  inconsistent  with  a number  of  facts 
which  nave  been  explained  by  various,  and  in  most  cases,  well 


12 


established,  tneories. 

This  theory  also  gives  a consistent  explanation  of  the  resist- 
ance of  alloys.  Of  these  there  are  two  kinds,  those  wnicn  for m mixed 
crystals  ana  those  which  do  not.  In  the  latter  case  separate  crystal 
are  formed  of  the  two  metals  and  the  resistance  may  be  compared  from 
the  rule  of  mixtures.  In  the  other  case,  however,  mixed  crystals 
are  formed  which  combine  best  according  to  certain  proportions  of  the 
two  components.  That  in  some  cases  an  imperfect  fitting  of  tnese  dif li- 
ferent snaped  crystals  would  tend  to  make  the  gaps  larger  and  tnu3 
increase  the  resistance  can  easily  be  deduced.  in  such  a case  the 
resistance  of  an  alloy  might  be  greater  than  either  of  its  component 
parts.  That  the  alloy  is  not  affected  so  much  by  changes  in  tempera- 
ture is  explained  by  assuming  that  the  imperfect  fitting  of  atoms 
persists  as  the  temperature  is  decreased. 

hard  drawing  increases  the  resistance  of  metals  and  is  explained 
as  due  to  tne  breaking  up  of  the  crystal  grains  and  thus  making  the 
atoms  fit  more  imperfectly.  This  explanation  seems  adequate  even 
though  the  density  decreases  when  the  metal  is  hard  drawn. 

Hardness  is  caused  by  a staggering  of  atoms,  hence  the  increase; 
resistance  is  due  to  a greater  separation  of  atoms,  which  is  in  ac- 
cord with  the  facts. 

In  the  case  of  solid  bismuth  and  antimony  wnicn  are  abnormal, 
tne  increase  of  resistance  per  degree  rise  in  temperature  is  normal. 
This  is  because  tne  effect  of  temperature  overshadows  any  pure  volume 
effect  so  that  the  temperature  coefficients  are  nearly  the  same  for 
all  metals  irrespective  of  the  pressure  coefficient.  That  liquid 
bismuth  behaves  normally  is  probably  due  to  the  fact  that  tne  crystal 
structure  is  broken  down  and  then  the  metal  acts  like  any  other. 


13 


In  none  of  tne  work  done  by  Bridgeman  was  anything  found  that 
would  seem  inconsistent  witn  tne  "gap”  theory.  This,  however,  seems 
to  nave  wcnueri'ul  elastic  possibilities  so  tnat  any  case  may  be  ex- 
plained without  actually  contradicting  tne  tneory  itself. 

Though  not  referred  to  by  Bridgeman,  F.  Credner’s  (7)  work  on 
tne  effect  on  resistance  of  twisting,  bending  ana  drawing  would  fur- 
ther lend  weignt  to  tms  view.  From  a large  amount  of  data  he  found 
that  eacn  of  these  operations  greatly  increases  the  resistance. 
Tamrramwho  did  similar  work  gives  a three  fold  explanation:  formation 
of  space  between  individual  crystalline  units,  tne  alteration  of  the 
structure  in  tne  case  of  stretching,  ana  formation  of  spaces  on  tne 
gliding  surfaces  in  tne  case  of  twisting. 

IV.  EXPERIMENTS  WITH  MECHANICAL  FORCES  ON  ELECTRONS 

Various  attempts  have  been  made  to  throw  additional  light  upon 
the  subject  of  metallic  conduction  of  electricity  by  means  of  experi- 
ments in  wmcn  mechanical  forces  are  exerted  upon  the  electrons.  The 
earliest  of  these  were  made  when  the  ionic  theories  of  conduction 
prevailed.  I.  Bosi  (quoted  by  nail  (12))  in  1877  used  electrolytes 
of  sulphate  of  zinc  ana  sulpnate  of  copper  wnicn  he  caused  to  flow 
with  a velocity  of  10  to  12  cm.  per  second,  ne  reported  that  there 
was  considerable  difference  in  tne  resistance  when  the  current  flowed 
in  the  direction  of  motion  and  when  it  flowed  in  the  opposite  direc- 
tion. 

J.B.  Haywood  (12)  of  the  Harvard  Graduate  school,  repeating 
the  experiment  under  Professor  E.H.  nails’  supervision,  found  tnat 
no  such  larg£ effects  could  be  detected  and  indeed  if  any  effect  ex- 
isted, it  was  exceedingly  small. 


14 


A similar  experiment  with  electrolytes  of  different  kinds  was 
performed  by  J.  Nabl  (19).  His  results  show  that  there  was  practical- 
ly no  change  in  the  resistance  aue  to  changing  the  direction  of  the 
current  with  respect  tc  the  movement  of  the  electrolyte. 

Tolman,  Osgerby,  and  Stewart  (32)  used  an  acceleration  method. 

A tube  was  filled  with  potassium  iodide  and  suddenly  accelerated 
which  set  up  a difference  of  potential  between  the  two  ends.  When 
such  a tube  was  placed  around  the  rim  of  a bicycle  wheel  and  quickly 
started  a current  was  set  up.  This  is  explained  as  due  tc  the  fact 
that  tne  negative  iodide  atoms  are  heavier  tnan  the  positive  potas- 
sium ions  and  thus  set  up  an  e.m.f.  opposite  tc  the  direction  of  ro- 
tat ion. 

E.F.  Nichols  (20)  brought  forth  a new  aspect  by  rotating  a 
disk  of  aluminum  on  which  contacts  had  been  made  at  tne  center  and 
the  outer  edge.  The  object  of  this  experiment  was  to  determine  from 
the  e.m.f.  developed  and  the  change  in  resistance,  whether  the  posi- 
tive or  the  negative  charge  was  bound  in  the  case  of  metal.  Since 
the  ratio  of  e/m  is  different  for  positive  and  negative  particles, 
the  mass  must  be  different,  which  would  then  give  different  centrifu- 
gal forces  to  each.  His  apparatus  did  not  prove  sensitive  enough 
to  enable  him  to  detect  results  which  would  verify  his  theory  that 
negative  ions  were  tne  carriers  of  electricity.  Various  heating  ef- 
fects also  proved  to  be  complications,  obscuring  any  positive  con- 
clusions. 

The  acceleration  method  was  used  by  Tolman  and  Stewart  (32) 
with  metals.  Their  former  apparatus  was  modified  by  replacing  the 
tube  filled  with  an  electrolyte  by  a coil  of  wire.  When  this  was 
rotated  and  suddenly  stopped  there  was  a "kick"  in  the  connected 


15 


galvanometer,  explained  as  aue  to  the  momentum  of  the  electrons.  The 
experimental  results  seem  to  warrant  the  acceptance  of  the  free  elec- 
tron theory  ratner  than  the  doublet  theory,  for  it  is  more  probable 
that  free  electrons  could  be  given  a momentum  than  that  such  accele- 
ration would  in  any  way  produce  action  on  electric  doublets. 

Two  years  previous  to  the  worx  just  described  an  experimental 
investigation  was  carried  on  in  the  Physics  Laboratory  of  the  Univer- 
sity of  Illinois  by  Paul  L.  Bayley  (1).  In  this  work  the  coil  was 
rotated  uniformly  ana  the  change  of  resistance  caused  by  rotation 
noted.  The  results  were  quite  small  and  could  not  be  determined  very 
accurately;  though  in  general  the  resistance  was  larger  when  the  coil 
was  rotating.  ' Experimental  difficulties  in  the  form  of  poor  contact 
of  the  measuring  instruments  with  the  rapidly  moving  parts  were  not 
encouraging  for  further  experiments,  until  better  methods  of  connec- 
tion could  be  devised. 

V.  EXPERIMENTS  BY  THE  WRITER 

It  was  the  purpose  of  the  present  experiment  to  remove  the  dif- 
ficulty involved  in  tne  contact  and  to  extend,  if  possible,  the  re- 
sults obtained  by  Bayley.  It  was  hoped  thus  to  obtain  additional 
data  which  would  disclose  more  concerning  the  mechanism  of  metallic 
conduction. 

The  coil  consisted  of  a large  number  of  turns  of  insulated 
copper  wire.  No. 25  B.&  S.,  which  was  wound  in  a groove  in  the  edge 
of  a disk  made  from  one-inch  compressed  fibre.  Tne  average  diameter 
of  the  coil  was  28.5  cm.  Each  layer  of  wire  was  covered  with  shellac 
and  allowed  to  dry  before  the  succeeding  layer  was  wound,  thus  insur- 
ing perfect  insulation  with  all  the  wires  rigidly  bound  together. 


. 

■ 

. 


. 


- 


✓ 


. 


. I - 


16 


The  ends  of  the  wire  were  attached  to  plates  on  eitner  side  of  the 
disk  which  in  turn  were  rigidly  attached  to  tne  snaft  of  tne  wheel 
or  disk.  The  shaft  was  cut  at  the  middle,  sc  tnat  the  two  ends  were 
insular ed  from  each  otner.  The  arrangement  of  tne  various  parts  are 
shown  in  Fig. 1. 

In  order  that  there  might  be  no  possible  magnetic  effects,  all 
parts  of  tne  disk  and  bearings  were  made  of  non-magnet ic  substances, 
brass  was  found  best  adapted  for  the  metal  parts.  The  axle  itself 
turned  in  babbitt  bearings  which  were  set  on  dry  wood  pillars  and 
completely  insulated  from  each  other.  On  the  outer  end  of  tne  snaft 
a pulley  was  attached  to  wnich  a quarter  inch  leather  belt  trans- 
ferred the  power  from  a two-phase,  60-cycle,  440-volt  induction  motor 
which  was  used  in  order  to  prevent  any  possible  electromagnetic  in- 
duction effects. 

In  the  apparatus  used  by  Bayley  the  contact  with  the  revolving 
parts  was  made  by  means  of  a mercury  fountain  attached  to  a hollow 
tube  all  parts  of  which  were  amalgamated,  this  tube  acted  as  a brush 
to  collect  the  current.  This  contact  was  found  to  be  very  unsatis- 
factory by  Bayley  particularly  at  high  speeds,  because  thermoelectric 
forces  were  produced  and  it  was  also  variable  in  action.  Another 
method  was  therefore  used  in  the  present  experiments.  A tapering 
hole  was  carefully  drilled  along  the  axis  of  the  shaft  at  each  end 
and  into  this  a brass  plug  which  could  easily  be  removed  was  fitted. 
At  the  center  of  the  plug  a copper  wire.  No. 25  B.&S. , was  soldered. 
This  wire  extended  outward  in  line  with  tne  axle  for  a distance  of 
fifty  feet  and  twisted  upon  itself  wnen  tne  coil  was  set  in  motion. 
This  is  tne  method  used  by  Tolman  and  Stewart.  In  this  experiment 
where  change  in  resistance  was  to  be  noted  instead  of  an  e.m.f.  or  an 


. 


. 


. 

. 

. 

■ 

' 

. 


. 

, . 


. 

. 

. ■ 

w 


C=i 


lr\ 


Seta.!'!  n_9  Wc£x~ 


Rubber 
Insu  lotion 


Pu/ ley 


Rotating  Coil 
C.C.  Schmidt 

May/ 92! 


n 


Coll 


W / re 


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Bea  rings 
— — ^ 


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niMi 

s 

111 

-^  / o 


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Sere  w 


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18 


instantaneous  current  sucn  an  arrangement  proved  very  unsatisfactory. 
It  was  found  that  there  was  a large  change  in  tne  resistance  of  the 
wire  when  it  was  twisted;  this  as  is  shown  also  in  the  work  of 
Tammam and  Credner  (7)  wnicn  has  been  mentioned  above. 

In  order  to  eliminate  this  effect  tne  wire  was  made  oniy  tnirty 
centimeters  long  and  passed  through  a tube  containing  mercury.  The 
ends  of  the  tube  were  stopped  and  the  wire  passed  through  the  stop- 
per at  each  end  and  then  fastened  to  a small  swivel  and  kept  taut  by 
a spring.  In  this  way  tne  wire  was  made  to  spin  in  the  mercury  bath 
when  the  disk  was  rotated.  This  device  proved  a very  satisfactory 
means  of  connecting  tne  fixed  part  of  the  circuit  witn  the  revolving 
coil  as  tne  results  snow.  The  cnange  in  resistance  was  quite  constats 
and  very  small  in  magnitude.  Tne  actual  change  due  to  the  rotation 
of  tne  connections  could  be  determined  by  inserting  a screw  which 
connected  the  brass  plates  on  tne  two  faces  of  the  disk;  this  made  a 

snort  circuit  around  the  coil.  The  effect  of  rotation  on  the  resist- 
% 

ance  of  the  contact  could  thus  be  determined  and  allowance  made  for 
the  same. 

When  tne  first  measurements  were  taken  with  the  coil  at  rest, 
it  was  found  that  very  slight  changes  in  temperature  caused  a very 
noticeable  change  in  the  resistance  as  was  determined  with  a Carey 
Foster  bridge.  Considerable  time  was  then  spent  in  finding  a room 
where  the  temperature  change  would  be  as  small  as  possible.  A 
double  walled  room  ordinarily  used  for  sound  determinations  was 
finally  used.  To  show  how  sensitive  the  coil  was  it  may  be  noted 
that  the  presence  of  one  person  cr  the  lighting  of  an  ordinary  elec- 
tric light  could  be  detected  by  tne  cnange  in  resistance  . 

A representative  curve  of  the  determination  of  tne  resistance 
of  this  coil  are  shown  in  Fig. 2.  The  resistance  is  plotted  as  the 


. 


•« 

. 


I 


■ 


20 


ordinate  ana  tne  time  as  tne  abscissae.  it  shows  a graaual  cnange 
in  tne  resistance  while  the  coil  is  being  rotated,  wnich  was  inter- 
preted as  due  to  temperature  changes  since  copper  has  a large  temper- 
ature coefficient  of  resistance.  A second  coil  was  made  using  manga- 
nin  wire.  The  results  were  of  similar  character,  but  the  changes  were 
much  less. 

Later  the  manganin  was  replaced  by  85.0b  meters  of  "Advance” 
wire  obtained  from  the  Driver-tiarris  Company.  This  was  not  shel- 
lacked during  the  winding  because  the  ordinary  insulation  was  suffi- 
cient for  the  small  electromotive  forces  used,  in  order  to  make  the 
wire  coil  rigid  ana  to  guard  against  any  possible  stretching,  due  to 
centrifugal  force,  which  would  of  course  tend  to  increase  the  resist- 
ance, n elted  sealing  wax  was  poured  into  the  groove  over  tne  wire. 
After  tnis  was  smootniy  turned  down  in  a latne  a hickory  rim  was 
bent  into  a circle  and  bound  closely  upon  tne  rim  of  the  disk  by  brass 
bands.  In  this  way  the  wire  was  held  rigidly  in  place. 

When  tnis  new  coil  was  rotated  a relatively  large  increase  of 
resistance  was  noted.  Since  "Advance"  wire  nas  a very  small  tempera- 
ture coefficient,  and  that  negative  (-.U000056),  such  an  effect  could 
not  be  explained  as  a temperature  cnange  in  tne  resistance  of  the 
wire,  hence,  another  source  of  the  effect  was  sougnt.  Since  it  con- 
tinued after  the  rotation  ceased  it  was  suspected  to  be  due  to 
thermo-electric  forces.  To  test  this,  a sensitive  galvanometer  was 
placed  in  series  with  the  coil;  then  a heated  block  of  brass  was 
placed  in  contact  with  the  bearing  and  also  with  the  pulley.  Each 
of  these  gave  a deflection.  By  placing  the  heated  block  on  the  con- 
tacts between  the  wire  and  the  brass  piares  similar  results  were  ob- 
tained. It  was  evident  that  though  the  disk  was  apparently  symmetri- 
cal, one  side  was  heated  more  tnan  the  ocher,  either  by  the  friction 


. 


. 

. 


. 


. 

. 

. 

. 

. 

.. 


. 


21 


in  the  bearings  or  else  by  friction  of  the  belt  on  the  pulley.  This 
unsymmetrical  heating  ana  the  consequent  thermo-electromotive  force 
was  the  cause  of  this  irregularity.  Hence,  the  disk  was  remodeled. 

Fig. 3 shows  the  remodeled  form  of  the  disk.  Two  radical 
changes  were  made:-  first  the  babbitt  bearings  were  replaced  by  high 
speed  ball  bearings  of  the  S.K.F.  type,  thus  reducing  the  friction 
to  practically  nothing;  furthermore,  the  brass  was  taken  out  as  a 
metal  of  the  circuit  by  drilling  a hole  along  the  axis  of  the  shaft 
and  another  through  the  brass  plate  perpendicular  to  the  shaft. 

Through  this  passage  an  insulated  copper  was  drawn.  The  brass  plug 
was  removed  and  replaced  by  one  of  copper  which  was  insulated  from 
the  brass  shaft  by  a hard  rubber  bushing.  In  this  way  the  thermo- 
junctions  between  brass  and  the  other  metals  were  removed.  The 
junctions  between  the  copper  and  "Advance”  wire  were  placed  on  eithei 
side  of  the  disk  as  near  the  outer  edge  of  the  disk  as  possible.  It 
would  be  very  unlikely  that  under  these  conaitions  the  two  junctions 
would  be  at  temperatures  noticeably  different.  In  fact,  no  thermo- 
electric forces  existed  at  these  points  after  these  changes  were  mads. 
In  order  that  the  coil  could  be  short  circuited  a fine  copper  wire 
was  soldered  to  the  plugs,  which  could  be  connected  to  small  screws 
near  the  ends  of  the  shaft. 


23 


TABLE  I 

SHOWING  EFFECT  OF  ROTATION  ON  RESISTANCE  OF  THE  COIL 


Resistance  of  Coil 
at  Rest 

235.87S04  ohms 
235. 88446 
235.92873 
Mean 
235.8970 


Resistance  of  Coil 
Rotating  Speed  7188  RPM 


Simultaneous  Observation 
of  e. m.  f . in  volts 

None 

less  than  -.000005  volts 
less  tnan  .000005 


Observat ions 
of  e.m.f. 


+.000015  volts 
. 000015 
.000007 
. 000006 
. 000015 


236.218345  ohms 
236.216986 
236.317893 
236.21699 0 
236.221055 
Mean 

236.318073 

Increase  in  resistance  of  coil  when  rotating  and  at  rest 

.3210  ohms. 

Table  I includes  some  of  the  results  showing  the  resistance 
while  at  rest  and  while  rotating  at  a speed  of  over  7000  RPM.  From 
the  data  it  may  be  seen  that  the  total  change  in  resistance  is  .321 
ohm.  The  e.m.f.  which  was  produced  while  the  coil  was  rotating  is 
shown  also.  This  was  measured  by  means  of  a Wolff  potentiometer. 

The  resistance  and  the  potential  could  be  found  almost  simultaneous!; 
by  throwing  a switch,  making  connections  first  with  the  Wrclff  poten- 
tiometer and  then  with  the  Carey  Foster  bridge.  The  reason  for  nctilg 


* 

, 

. 

. 

. • . 

. 


24 

the  e.m.f.  was  to  have  a cneck  on  any  thermo-electric  forces  which 
might  he  present. 

There  seems  no  direct  relation  between  this  change  of  resist- 
ance and  the  small  e.m.f.  which  was  detected.  It  is  thought  that 
these  were  largely  due  to  contacts  outside  of  the  disk  for  similar 
effects  were  noted  wnen  the  coil  was  short  circuited.  In  order  to 
determine  wnat  influence  these  electromotive  forces  might  have  on 
the  resistance,  the  current  in  the  Carey  Foster  bridge  was  reversed; 
the  effect  of  this  is  shown  in  Table  II. 

TABLE  II 

SHOWING  EFFECT  OF  REVERSING  BATTERY  OF  CAREY  FOSTER  BRIDGE 

Resistance  of  Coil  at  Re3t 

Current  Direct  Current  Reversed  Difference  e.m.f.  Observed 
235,92873  ohms  235.92873  ohms  0 0 

Resistance  of  Coil  Rotating  7188  R. P.M. 

236.21834  ohms  236.21608  ohms  .00226  .000015  volt 

236.21789  ohms  236.21699  ohms  .00090  .000015  volt 

Mean  .00155  ohm 

Since  the  e.m.f.  was  always  in  the  same  direction  this  snows 
that  the  maximum  change  in  resistance  due  to  this  source  is  only 
.00226  ohm  and  that  this  is  actually  twice  as  great  as  tne  true  ef- 
fect, for  here  a difference  was  taken  between  the  resistance  plus 
the  effect  ana  the  resistance  minus  the  effect  of  the  e.m.f.  The 

true  value  for  the  maximum  value  observed  is  only  .00113. 

To  make  further  correction  the  resistance  due  to  the  mercury 
contact  must  be  considered.  The  actual  resistance  of  the  system 
when  the  coil  is  cut  out  by  tne  short  circuiting  device  is  .20371 
ohm  wnen  at  rest,  and  .213099  ohm  when  tne  wneel  is  rotating. 


. . . 


25 


showing  that  a change  of  .010828  ohm  is  due  to  the  contact  alone. 

Deducting  tnese  two  measurable  effects  from  the  observed  change 
in  resistance  tne  data  may  be  summed  up  as  follows: 

Gross  change  in  resistance  .3210 

Change  due  to  e.m.f.  .00155 

Change  due  to  contacts  . 010828 

.012378  .012378 

Corrected  change  in  resistance  .309622  chm 

which  is  a change  of  1.38$  of  the  total  resistance  of  the  coil. 

While  these  observations  were  being  made  with  tne  Advance  wire 
coil,  the  original  copper  coil  was  Changed  and  the  connections  made 
independent  of  the  brass  parts.  It  was  found,  however,  that  this  wan 
so  sensitive  to  temperature  changes  due  to  the  high  temperature 
coefficient  of  copper,  that  no  reliable  results  of  the  effect  of  ro- 
tation could  be  obtained.  When  it  is  considered  that  the  linear  ve- 
locity of  the  coil  is  about  225  miles  per  hour,  or  105  meters  per 
second,  the  tremendous  amount  of  air  friction  may  be  realized  and  it 
is  thought  that  the  greater  part  of  the  change  in  resistance  (over 
4 ohms  was  observed)  was  largely  due  to  a heating  effect.  That  ther< 
was  no  thermo-electric  effect  was  shown  from  the  fact  that  the  elec- 
tromotive force  measured  with  the  potentiometer  was  very  slight. 

The  elimination  of  this  temperature  effect  is  very  desirable 
and  it  may  be  possible,  though  at  present  it  offers  the  chief  diffi- 
culty in  the  determination  of  the  effect  of  rotation  on  the  resist- 
ance of  pure  metals. 


One  ppssible  source  of  error  whose  weight  could  not  be  deter- 
mined was,  that  though  all  precautions  were  taken  to  make  the  wire 
coil  rigid,  there  is  a possibility  that  the  disk  as  a whole  expanded 


. . . 


. 


. 


. 

. 

. 

I 

. 


36 


thus  causing  a stretching  of  the  wire  which  would  undoubtedly  in- 
crease the  resistance.  But  with  the  disk,  made  up  as  it  is  with  hea\|Jr 
brass  plates  on  each  side  for  a quarter  of  the  diameter,  and  finally 
bound  with  outer  rims  of  sealing  wax  and  hickory,  it  hardly  seems 
possible  that  there  is  any  appreciable  stretch  of  the  disk.  Tests 
must,  however,  be  made  for  any  possible  stretching  effect. 


VI.  SUMMARY  AND  CONCLUSIuNS 

1.  A method  has  been  devised  by  which  practically  constant 
electric  connections  can  be  made  with  a coil  revolving  at  a speed  of 
over  7000  RPM.  The  change  in  resistance  from  rest  to  full  speed 
due  to  this  contact  is  a very  small  amount,-  in  this  case  only  .0108 
ohm. 

2.  The  thermo-electric  forces  produced  in  the  system  have 
been  reduced  to  a very  small,  practically  negligible  quantity.  In 
the  final  results  1 /3$>  of  the  total  change  of  resistance  could  be 
traced  as  possibly  due  to  thermo-electric  forces. 

3.  It  has  been  shown  that  the  resistance  of  a coil  of  Advance 
wire  is  increased  by  rotation  at  a speed  of  7000  RPM.  The  change  of 
resistance  When  allowance  is  made  for  other  known  effects  is  .309 
ohm,  or  1.38%  of  the  total  resistance.  The  centrifugal  acceleration 
in  this  case  is  763,000  cm.  per  sec.  per  sec. 

4.  Experiments,  similar  to  those  made  with  " Advance"  wire, 
with  a copper  wire  showed  temperature  effects  too  great  to  allow  any 
deductions  as  to  the  effect  of  rotation  alone.  The  elimination  of 
this  temperature  effect  is  the  next  step,  as  it  is  very  desirable 

to  get  results  with  a pure  metal. 


5.  It  is  not  easy  to  analyze  the  results  of  this  experiment 


* 


. 


- 


. 

. 


. 


; 


. 


. 


. 

. 


27 


as  to  its  bearing  upon  the  theory  of  metallic  conduction,  because  it 
does  not  point  conclusively  to  any  one  of  the  tneories  advanced.  The 
results  are,  however,  more  easily  explained  on  the  "free  gas"  or  the 
"doublet"  theory  than  on  the  "gap”  theory. 

a.  If  we  are  to  accept  the  free  electron  tneory,  tnen  tne 
change  of  resistance  might  be  explained  by  assuming  that  the  elec- 
trons are  thrown  to  the  outer  portion  of  the  conductor,  thus  produc- 
ing a crowding  or  condensation  of  tne  electrons,  which  would  cause 
an  increase  in  tne  number  of  collisions  or  the  friction  between  the 
electrons  and  tne  molecules. 

b.  According  to  tne  doublet  theory  suen  a force  might  tend  to 
depolarize  the  dipoles  or  to  throw  tne  chain  of  doublets  out  of  line 
which  would  cause  tne  resistance  to  become  greater. 

c.  If  a stretching  effect  of  the  wire  could  be  detected  then 
such  a change  in  resistance  might  be  explained  from  the  "gap»  tneory 
whicn  seems  to  cover  quite  extensively  tne  cnanges  of  resistance  due 
to  cnanges  in  the  structure  of  a metal.  But  the  possioility  of  a 
stretching  of  tne  coil,  as  already  noticed,  seems  to  be  very  small. 

If  the  increase  is  due  to  a pure  rotation  effect  then  it  is  hard  to 
see  how  it  can  be  explained  on  any  "gapn  theory. 

The  fact,  that  tne  results  obtained  are  entirely  from  "Advance* 
wire  which  is  an  alloy  and  nence  involves  factors  not  present  in 
pure  metals,  prevents  definite  conclusions  as  to  tne  effect  of  a 
similar  experiment  upon  a pure  metal. 

The  writer  wisnes  to  thank  Professor  A.P.  Carman  for  his  int- 
erest and  encouragement  in  the  experimental  work  ana  the  valuable 
assistance  given  in  the  preparation  of  this  manuscript. 


. 


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. 

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' 


. 


. 


. 

. . 


. 


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